To estimate the maximum tolerated and dose-limiting toxicities of irinotecan administered over 90 min, weekly x 4, every 6 weeks in children with refractory or progressive solid tumors. To determine the pharmacokinetics of irinotecan and its active metabolite SN-38 administered over 90 min, weekly x 4, every 6 weeks to children with refractory or progressive cancer. To determine the pharmacokinetics of irinotecan and its active metabolite SN-38 administered weekly x 4, every 6 weeks to children with refractory or progressive cancer who are receiving concomitant anticonvulsants. Six patients have been accrued at the initial dose level (125 mg/m2/dose). Dose escalation to 150 mg/m2/dose is planned pending toxicity evaluation of the patients enrolled at the first dose level.